Week 8 - Natural Convection-II

I. Aim

To buid the model for a low-voltage control-panel, as per the given specifications, and perform steady-state thermal analysis of the same.

II. Introduction

In the current project, the following tasks are performed:

1. The model for a low-voltage control panel is created in ANSYS Icepak using the following given information:

1.1. The images attached below show the single-line diagram of the network and the schematic of the switchboard/control-panel.

1.2. The given dimensions of the control-panel are as follows: height 2000 mm, width 800 mm and depth 900 mm

1.3. The total incoming current to the control-panel is 1214 A. The images attached below show the circuit-breaker losses (table 7.13), current distribution (table 7.14) and busbar dimensions (table 7.14).

2. The computational domain is meshed using non-conformal meshing.

3. The following physical phenomena are incorporated in the model:

3.1. Joule heating in the current carring busbars

3.2. Natural convection (buoyancy-induced flow)

3.3. Turbulence in the flow-field

3.4. Radiation heat transfer

4. The steady-state governing equations for the model are solved using the Fluent solver available in ANSYS Icepak, to determine the flow-field and thermal-field within the computational domain.

A low-voltage control-panel is a component in the electrical distribution system that allocates the incoming current feed to different electrical-circuits within a facility. It houses circuit-breakers for every branch-circuit to protect them against electrical overloads and short circuits. Thermal simulation of the control-panels, similar to the current simulation, is often performed by the thermal engineers working in the electrical industry to determine whether any component inside the control-panel is exceeding its thermal imit.

III. Geometry

The complete model of the control-panel is created in ANSYS Icepak using the following steps:

1. Busbars and circuit-breakers: They form the internal components of the control-panel and are created, as per the given dimensions, using multiple "Blocks" objects available in Icepak. The dimensions and locations of the circuit-breakers are assumed appropriately. The images attached below show the geometry settings used to define one of each of the busbars and the circuit-breakers.

i. Busbar-D

ii. Circuit-breaker IG

All the internal components (busbars and circuit-breakers) are assigned the same solid material ("Cu-Pure") and surface material ("Cu-polished-surface"). Joule heating with "Constant" power type setting is enabled for the busbars and they are assigned currents based on the given specifications. The circuit-breakers are assigned constant thermal dissipation values based on the given specifications. The images attached below show the settings applied in the "Properties" tab to define one of each of the busbars and the circuit-breakers.

i. Busbar-D

ii. Circuit-breaker IG

The image attached below shows all the busbars and circuit-breakers that are located within the control-panel.

2. Control-panel: It houses the current carrying components (busbars) and circuit-breakers and is created using the "Enclosure" object available in Icepak, as per the given outer dimensions. "Steel-Carbon-1020" and "Paint-white-acrylic" are used as the solid material and the surface material respectively, for the control-panel. Each wall of the control-panel is assigned a "Thin" type boundary condition and a thickness of 2 mm. Radiation heat transfer is enabled for all the walls of the control-panel. The images attached below show the settings applied in the "Geometry" and "Properties" tabs, to define the control-panel.

i. Geometry

ii. Properties

Two grilles are defined on a pair of opposite walls of the control-panel to allow: the ambient air to move into the control-panel and the air inside the control-panel to move out of it. The grille for the intake of ambient air is placed near the base of the control-panel while the grille for the output of hot air is placed near the top of the control-panel. Hence the two grilles allow air-cooling of the heat generating components (located inside the control-panel) due to natural convection. The image attached below shows the control-panel.

3. Cabinet: It encloses the computational domain of the simulation. In order to perform a natural convection simulation, adequate spacing is provided between the control-panel and the cabinet. All the cabinet walls are defined using the "Opening" type boundary condition except the bottom wall (which overlaps the base of the control-panel) which is defined using the "default" type boundary condition. The images attached below show the settings applied in the "Geometry" and "Properties" tabs to define the cabinet.

i. Geometry

ii. Properties

The image attached below show the complete geometry of the model.

IV. Meshing

The following meshing techniques are utilized in the current project to discretize the computational domain:

1. Non-conformal meshing technique allows the user to selectively refine the mesh within a sub-region around an assembly by selecting the "Mesh separately" option available in the "Meshing" tab of the assembly settings. A comparatively coarse mesh can be used for the rest of the model. Multiple assemblies, that employ non-conformal meshing, are defined in the model. The image attached below shows the settings applied in the "Meshing" tab to define one such assembly.

2. The "Object params" option available in the "Mesh control" window allows the user to refine the mesh locally near one or more objects/assemblies defined in the model. "Per-object meshing parameters" are specified for the assembly defined around the control-panel in the current model. The image attached below shows the settings applied in the "Per-object meshing parameters" window for the assembly.

After completing the above steps, the computational mesh is generated. The image attached below shows the "Mesh control" window.

The image shows that the generated mesh yields 526360 elements and 775952 nodes. The images attached below show the computational mesh on three mutually perpendicular planes, each passing through the center of the cabinet.

i. X-plane

ii. Y-plane

iii. Z-plane

The images attached below show the volume mesh on the components located inside the control-panel: busbars and circuit-breakers.

Visually the mesh appears to be fine. The images attached below show the histograms with the number of elements plotted along the X-axis and the quality measures plotted along the Y-axis.

1. Face alignment

Values less than 0.05 indicate the presence of severely distorted elements in the mesh. All the elements in the current mesh have a face alignment of 1 which indicates that they are perfectly aligned to each other.

2. Volume

For a double precision solver, the minimum cell-volume shouldn't be less than 1e-15 m^3 otherwise the solver may face issues. The minimum cell-volume in the current mesh is 3.7037e-8 m^3 and hence the mesh elements aren't small enough to cause problems in the solver.

3. Skewness

A skewness of 0 indicates that the mesh element is degenerate whereas a skewness of 1 indicates that the mesh element is ideal (equilateral/equiangular). All the elements in the current mesh have a skewness of 1 which indicates that they are ideal (equilateral/equiangular).

V. Solver

The three-dimensional steady-state Navier-Stokes equations for the model are solved within the computational domain using the Fluent solver available in ANSYS Icepak. The following settings are applied to the solver:

1. Variables solved: Flow (velocity, pressure) and Temperature

2. Radiation: On

2.1. Model: Surface to surface radiation model

3. Flow regime: Turbulent

3.1. Model: Zero equation model

4. Time variation: Steady

5. Solution initialization

5.1. X velocity: 0

5.2. Y velocity: 0.000980665 m/s

5.3. Z velocity: 0

5.4. Temperature: Ambient (20 deg. C)

6. Natural convection

6.1. Density model: Boussinesq approximation

6.2. Operating pressure: 101325 N/m2

6.3. Operating density: 1.225 Kg/m3

6.4. Gravity vector: 9.80665 m/s^2 directed along the negative Y-axis

7. Number of iterations: 1000

8. Convergence criteria

8.1. Flow: 1e-7

8.2. Energy: 1e-7

8.3. Joule heating: 1e-7

9. Configuration: Parallel

10. Number of processors: 4

11. GPU computing: Enabled

12. Number of GPUs: 1

13. Discretization scheme

13.1. Pressure: Standard

13.2. Momentum: First

13.3. Temperature: First

14. Under-relaxation factors

14.1. Pressure: 0.3

14.2. Momentum: 0.7

14.3. Temperature: 1

14.4. Viscosity: 1

14.5. Body forces: 1

14.6. Joule heating potential: 1

15. Linear solver settings

15.1. Pressure - Type: V, Termination criterion: 0.1, Residual reduction tolerance: 0.7, Stabilization: None

15.2. Momentum - Type: flex, Termination criterion: 0.1, Residual reduction tolerance: 0.7

15.3. Temperature - Type: F, Termination criterion: 0.1, Residual reduction tolerance: 0.7, Stabilization: None

15.4. Joule heating potential - Type: F, Termination criterion: 0.1, Residual reduction tolerance: 0.7, Stabilization: None

16. Precision: Double

VI. Results

In the current section, the simulation results are discussed.

1. Residuals

The residuals of the following equations are plotted against the number of iterations:

i. Continuity equation

ii. X-Momentum equation

iii. Y-Momentum equation

iv. Z-Momentum equation

v. Energy equation

The image attached below shows the residuals plotted against the number of iterations.

The plot shows that the residuals are quite small quantitatively and don't change appreciably between 800-1000 iterations thereby indicating that the solution has reached a steady state. In the current project, the simulation results after 1000 iterations are considered as steady-state results.

2. Monitor plots

Monitor points are probes set up at various key locations within the computational domain to determine the solution variables (such as pressure, velocity, temperature etc.). Data obtained from monitor points can also be used to ascertain whether the solution has reached a steady state. In the current project the following monitor ponts are created:

i. IG: Temperature monitor point

ii. I1: Temperature monitor point

iii. I2: Temperature monitor point

iv. I3: Temperature monitor pont

v. I4: Temperature monitor point

vi. I5: Temperature monitor point

vii. grille.1: Velocity monitor point

viii. grille.2: Velocity monitor point

The images attached below show the data obtained from the monitor points, plotted against the number of iterations.

2.1. Temperature monitor points

2.2. Velocity monitor points

The plots show that the monitored values don't change appreciably after 500 iterations. This further confirms that the simulation results after 1000 iterations are steady-state results. The following steady-state values are predicted by the plots:

i. IG: 65.13 deg. C

ii. I1: 42.15 deg. C

iii. I2: 41.29 deg. C

iv. I3: 41.04 deg. C

v. I4: 41.24 deg. C

vi. I5: 41.04 deg. C

vii. grille.1: 0.10 m/s

viii. grille.2: 0.10 m/s

3. Velocity contours

The steady-state velocity contours are plotted on the X-plane passing through the center of the cabinet, as shown in the image attached below.

The plot shows that the air within the computational domain is in a state of motion. This can be attributed to natural convection which drives the air upwards, against the gravitational field, due to the difference in density created by the virtue of temperature difference. According to the contour-legend the maximum air-velocity on the X-plane passing through the center of the cabinet is 0.35 m/s.

4. Velocity vectors

The steady-state velocity vectors are plotted on the X-plane passing through the center of the cabinet, as shown in the image attached below.

The plot shows the velocity vectors for air plotted at 10000 points distributed uniformly throughout the X-plane passing through the center of the cabinet. The velocity vectors clearly show that the air in the computational domain is rising upwards as a consequence of natural convection. It can be seen that air enters into the control-panel through the lower grille and leaves it through the upper grille. This constant air-current established due to natural convection is responsible for dissipating the heat generated in the busbars and the circuit-breakers.

5. Temperature contours

The steady-state temperature contours are plotted on the X-plane passing through the center of the cabinet, as shown in the image attached below.

The plot shows that the air within the computational domain is cooler than any other object. It can be seen that the temperature of the air within the computational domain increases as we move up (against gravity). This can be explained in the following manner: the air that is in direct contact with the comparatively hotter objects takes up their heat due to which its temperature increases and its density decreases. Under the influence of the downward gravitational field, this lighter (hotter) air rises up and the surrounding heavier (cooler) air rushes in to fill up the evacuated space.

6. Object face temperature contours

The steady-state temperature contours are plotted on all the objects in the model that are located inside the control-panel (the busbars and the circuit-breakers), as shown in the image attached below.

The contours show that the circuit-breaker IG attains the highest steady-state temperature, followed by busbar-B, busbar-C, the remaining circuit-breakers and the remaining busbars respectively.

7. Particle traces

The steady-state particle traces (colored by temperature) of 100 particles that originate at the lower grille of the control-panel are plotted within the computational domain, as shown in the animation attached below.

The animation clearly shows the steady-state pathlines traced by air particles, that originate at the lower grille of the control-panel, within the computational domain. The color of a pathline at a particular location indicates the temperature of the air particle that traces the pathline, at that location.

VII. Conclusion

In the current project, the model of a low-voltage control-panel was created in ANSYS Icepak using the given design-specifications. The model was meshed using the following features available in the Icepak mesher: non-conformal meshing and per-object meshing parameters. The solver was setup using suitable settings to incorporate the following physical phenomena:

i. Joule heating

ii. Natural convection

iii. Turbulence

iv. Radiation heat transfer

The three-dimensional steady-state governing equations for the model were solved for flow and thermal fields within the computational domain using the Fluent solver available in ANSYS Icepak. The following conclusions can be drawn based on the simulation results:

i. Both the residual plot and the monitor plot show that the simulation results after 1000 iterations can be considered as steady-state results.

ii. According to the steady-state velocity contours, the maximum velocity within the computational domain is 0.35 m/s.

iii. The highest steady-state temperature within the computational domain is attained by the circuit-breaker IG and its numerical value is 65.13 deg. C.

iv. The following steady-state temperatures are attained by the circuit-breakers:

(a) IG: 65.13 deg. C

(b) I1: 42.15 deg. C

(c) I2: 41.29 deg. C

(d) I3: 41.04 deg. C

(e) I4: 41.24 deg. C

(f) I5: 41.04 deg. C